A safety system for the protection of vehicle occupants is known from the article by W. Suchowerskyj, entitled “Evolution en matiére de detecteurs de choc” (Development of impact sensors), in 1141 Ingénieurs de l'Automobile (1982) No. 6, pages 69 through 77, Paris, for example. Acceleration-sensitive sensors are essentially used as crash sensors in such safety systems. The evaluation of their output signals should make it possible to recognize dangerous crashes as early as possible in order to trigger safety measures in the event of danger, in particular deployment of restraining means for the vehicle occupants. However, even after the introduction of the airbag, serious or even deadly injuries of vehicle occupants have regrettably occurred time and again, despite relatively low speeds. In most of those cases, the vehicle occupants were not buckled up or were placed very close in front of the airbag module used as restraining means. In order to provide the vehicle occupants with optimum protection in the event of an accident, it is necessary to know both the upper body and head positions of the vehicle occupant prior to the ignition of the airbag. It is known to determine the position and motion dynamics of vehicle occupants using IOS sensors (video camera, OC mat (occupant classification), force measuring pin, strain gauge, etc.) and to classify the occupant (German Patent Application No. DE 102 33 098) with the aid of the knowledge of the accelerations acting upon the occupant in both the x and y directions (DIN 70000). Moreover, it is also possible to predict the trajectory of an occupant (German Patent Application No. DE 102 46 255) using the same information (occupant dynamics and accelerations).